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/* Copyright (c) 2008-2022 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#ifndef __math_cubic_spline_h__
#define __math_cubic_spline_h__
namespace MR
{
namespace Math
{
enum SplineProcessingType
{
Value = 1,
Derivative = 2,
ValueAndDerivative = Value | Derivative
};
template <typename T> class CubicSpline
{ MEMALIGN(CubicSpline<T>)
public:
using BasisMatrix = Eigen::Matrix<T, 4, 4>;
using WeightVector = Eigen::Matrix<T, 1, 4>;
WeightVector weights, deriv_weights;
void set (T position) {
(this->*(_internal_set)) (position);
}
T coef (size_t i) const {
return (weights[i]);
}
protected:
static const BasisMatrix cubic_poly_derivative_operator;
const BasisMatrix basis_matrix;
const BasisMatrix deriv_basis_matrix;
CubicSpline (SplineProcessingType processType, const BasisMatrix basis_matrix, const BasisMatrix deriv_basis_matrix) :
basis_matrix (basis_matrix),
deriv_basis_matrix (deriv_basis_matrix)
{
switch (processType) {
case SplineProcessingType::Value:
_internal_set = &CubicSpline::_set_value;
break;
// Could be used for partial derviative so we need to calculate both deriv and value weights
case SplineProcessingType::Derivative:
case SplineProcessingType::ValueAndDerivative:
_internal_set = &CubicSpline::_set_value_deriv;
break;
default:
break;
}
}
private:
CubicSpline () {}
// Function pointer to the internal set function depening on processing type
void (CubicSpline::*_internal_set) (T);
inline void _set_value (T position) {
const T p2 = Math::pow2(position);
const auto vec = WeightVector (p2 * position, p2, position, 1.0);
weights = (vec * basis_matrix);
}
inline void _set_value_deriv (T position) {
const T p2 = Math::pow2(position);
const auto vec = WeightVector (position * p2, p2, position, 1.0);
weights = (vec * basis_matrix);
deriv_weights = (vec * deriv_basis_matrix);
}
};
// Hermite spline implementation
template <typename T> class HermiteSpline :
public CubicSpline<T> { MEMALIGN(HermiteSpline<T>)
public:
using BasisMatrix = typename CubicSpline<T>::BasisMatrix;
static const BasisMatrix hermite_basis_mtrx;
static const BasisMatrix hermite_derivative_basis_mtrx;
HermiteSpline (SplineProcessingType processType)
: CubicSpline<T> (processType, hermite_basis_mtrx, hermite_derivative_basis_mtrx) {}
};
// Uniform bspline implementation
template <typename T> class UniformBSpline :
public CubicSpline<T> { MEMALIGN(UniformBSpline<T>)
public:
using BasisMatrix = typename CubicSpline<T>::BasisMatrix;
static const BasisMatrix uniform_bspline_basis_mtrx;
static const BasisMatrix uniform_bspline_derivative_basis_mtrx;
UniformBSpline (SplineProcessingType processType)
: CubicSpline<T> (processType, uniform_bspline_basis_mtrx, uniform_bspline_derivative_basis_mtrx) {}
};
// Initialise our static const matrices
template <typename T>
const typename CubicSpline<T>::BasisMatrix
CubicSpline<T>::cubic_poly_derivative_operator((BasisMatrix() <<
0, 0, 0, 0,
3, 0, 0, 0,
0, 2, 0, 0,
0, 0, 1, 0).finished());
// Hermite spline
template <typename T>
const typename HermiteSpline<T>::BasisMatrix
HermiteSpline<T>::hermite_basis_mtrx((BasisMatrix() <<
-0.5, 1.5, -1.5, 0.5,
1, -2.5, 2, -0.5,
-0.5, 0, 0.5, 0,
0, 1, 0, 0).finished());
template <typename T>
const typename HermiteSpline<T>::BasisMatrix
HermiteSpline<T>::hermite_derivative_basis_mtrx(CubicSpline<T>::cubic_poly_derivative_operator * hermite_basis_mtrx);
// Uniform b-spline
template <typename T>
const typename UniformBSpline<T>::BasisMatrix
UniformBSpline<T>::uniform_bspline_basis_mtrx((1/6.0) * (BasisMatrix() <<
-1, 3, -3, 1,
3, -6, 3, 0,
-3, 0, 3, 0,
1, 4, 1, 0).finished());
template <typename T>
const typename UniformBSpline<T>::BasisMatrix
UniformBSpline<T>::uniform_bspline_derivative_basis_mtrx(CubicSpline<T>::cubic_poly_derivative_operator * uniform_bspline_basis_mtrx);
}
}
#endif
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